Causal discounting and conditional reasoning in children (original) (raw)
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The Open Psychology Journal, 2010
This article traces the philosophical and psychological connections between causation and the conditional, if...then, across the two main paradigms used in conditional reasoning, the selection task and the conditional inference paradigm. It is argued that hypothesis testing in the selection task reflects the philosophical problems identified by Quine and Goodman for the material conditional interpretation of causal laws. Alternative formal theories to the material conditional only became available with the advent of possible worlds semantics . The relationship proposed by this semantics between counterfactual and indicative conditionals is outlined and it is concluded that moving away from the abstractions of possible worlds proposes a central role for prior knowledge in conditional inference. This conclusion is consistent with probabilistic approaches to conditional inference which provide measures of the strength of a dependency between the antecedent and the consequent of a conditional similar to those proposed in causal learning. Findings in conditional inference suggest that people are influenced not only by the strength of a dependency but also by the existence of the structural relationship, the broader causal framework in which a dependency is embedded, and the inhibitory and excitatory processes like those required to implement Causal Bayes nets or neural networks. That these findings may have a plausible explanation using the tools of current theories in causal learning suggests a potentially fruitful convergence of research in these two areas.
Causation and Conditionals in the Cognitive Science of Human Reasoning
The Open Psychology Journal, 2010
This article traces the philosophical and psychological connections between causation and the conditional, if...then, across the two main paradigms used in conditional reasoning, the selection task and the conditional inference paradigm. It is argued that hypothesis testing in the selection task reflects the philosophical problems identified by Quine and Goodman for the material conditional interpretation of causal laws. Alternative formal theories to the material conditional only became available with the advent of possible worlds semantics . The relationship proposed by this semantics between counterfactual and indicative conditionals is outlined and it is concluded that moving away from the abstractions of possible worlds proposes a central role for prior knowledge in conditional inference. This conclusion is consistent with probabilistic approaches to conditional inference which provide measures of the strength of a dependency between the antecedent and the consequent of a conditional similar to those proposed in causal learning. Findings in conditional inference suggest that people are influenced not only by the strength of a dependency but also by the existence of the structural relationship, the broader causal framework in which a dependency is embedded, and the inhibitory and excitatory processes like those required to implement Causal Bayes nets or neural networks. That these findings may have a plausible explanation using the tools of current theories in causal learning suggests a potentially fruitful convergence of research in these two areas.
Conditional reasoning and causation
An experiment was conducted to investigate the relative contributions of syntactic form and content to conditional reasoning. The content domain chosen was that of causation. Conditional statements that described causal relationships (if (cause>, then (effect>) were embedded in simple arguments whose entailments are governed by the rules-oftruth-functional logic (i.e., modus ponens, modus tollens, denying the antecedent, and affirming the consequent). The causal statements differed in terms ofthe number of alternative causes and disabling conditions that characterized the causal relationship. (A disabling condition is an event that prevents an effect from occurring even though a relevant cause is present.) Subjects were required to judge whether or not each argument's conclusion could be accepted. Judgments were found to vary systematically with the number of alternative causes and disabling conditions. Conclusions of arguments based on conditionals with few alternative causes or disabling conditionswerefoun~d:tobe-rnore accept~ able than cdnclusions based on those with many.
Theories of Conditional Reasoning: A Developmental Examination of Competing Hypotheses
Developmental Psychology, 2004
Children and adolescents were presented with problems that contained deontic (i.e., if action p is taken, then precondition q must be met) or causal (i.e., if event p occurs, then event q will transpire) conditionals and that varied in the ease with which alternative antecedents could be activated. Results showed that inferences were linked to the availability of alternative antecedents and the generation of "disabling" conditions (claims that the conditionals were false under specific circumstances). Age-related developments were found only on problems involving indeterminate inferences. Correlations among inferences differed for children and adolescents. The findings provide stronger support for domain-general theories than for domain-specific theories of reasoning and suggest, under some conditions, age-related changes in the roles of implicit and explicit processing.
Reasoning as we read: Establishing the probability of causal conditionals
Memory & Cognition, 2013
Indicative conditionals of the form if p then q (e.g., if student tuition fees rise, then applications for university places will fall) invite consideration of a hypothetical event (e.g., tuition fees rising) and of one of its possible consequences (e.g., applications falling). Since a rise in tuition fees is an uncertain event with equally uncertain consequences, a reader may believe the statement to a greater or lesser extent. As a conditional is read, the earliest point at which this probabilistic evaluation can take place is as the consequent clause is wrapped up (e.g., as the critical word fall is read in the example above). Wrap-up processing occurs at the end of the clause, as it is evaluated and integrated into the evolving discourse representation. Five sources of probability may plausibly influence the evaluation of a conditional as it is wrapped up; these are P(p), P(q), P(pq), P(q|p), and P(not-p or q). A total of 128 conditionals were constructed, with these probabilities calculated for each item in a pretest. The conditionals were then embedded in vignettes and read by 36 participants on a word-by-word basis. Using linear mixed-effects modeling, we found that wrap-up reading times were predicted by pretest ratings of P(p) and P(q|p). There was no influence of P(q), P(pq), or P(not-p or q) on wrap-up reading times. Our findings are consistent with the suppositional theory of conditionals proposed by Evans and Over (2004) but do not support the mental-models theory advanced by .
The mental representation of causal conditional reasoning: Mental models or causal models
Cognition, 2011
In this paper, two experiments are reported investigating the nature of the cognitive representations underlying causal conditional reasoning performance. The predictions of causal and logical interpretations of the conditional diverge sharply when inferences involving pairs of conditionals-such as if P 1 then Q and if P 2 then Q-are considered. From a causal perspective, the causal direction of these conditionals is critical: are the P i causes of Q; or symptoms caused by Q. The rich variety of inference patterns can naturally be modelled by Bayesian networks. A pair of causal conditionals where Q is an effect corresponds to a ''collider'' structure where the two causes (P i ) converge on a common effect. In contrast, a pair of causal conditionals where Q is a cause corresponds to a network where two effects (P i ) diverge from a common cause. Very different predictions are made by fully explicit or initial mental models interpretations. These predictions were tested in two experiments, each of which yielded data most consistent with causal model theory, rather than with mental models.
Journal of Experimental Psychology: Learning, Memory, & Cognition, 2003
- proffered a Bayesian model in which conditional inferences are a direct function of conditional probabilities. In the current article, the authors first considered this model regarding the processing of negatives in conditional reasoning. Its predictions were evaluated against a large-scale meta-analysis (W. J. Schroyens, W. . This evaluation shows that the model is flawed: The relative size of the negative effects does not match predictions. Next, the authors evaluated the model in relation to inferences about affirmative conditionals, again considering the results of a meta-analysis (W. J. Schroyens, W. . The conditional probability model is countered by the data reported in literature; a mental models based model produces a better fit. The authors conclude that a purely probabilistic model is deficient and incomplete and cannot do without algorithmic processing assumptions if it is to advance toward a descriptively adequate psychological theory.
The modulation of conditional assertions and its effects on reasoning
The Quarterly Journal of Experimental Psychology, 2010
The theory of mental models postulates that conditionals of the sort, if A then C, have a "core" meaning referring to three possibilities: A and C, not-A and C, and not-A and not-C. The meaning of a conditional's clauses and general knowledge can modulate this meaning, blocking certain possibilities or adding relations between the clauses. Four experiments investigated such interpretations in factual and deontic domains. In Experiment 1, the participants constructed instances of what was possible and what was impossible according to various conditionals. The results corroborated the general predictions of the model theory and also the occurrence of modulation. The resulting interpretations governed the conclusions that participants accepted in Experiment 2, which also yielded the predicted effects of a time limit on responding. In Experiment 3, the participants drew the predicted conclusions for themselves. In Experiment 4, modulation led to predicted temporal relations between A and C. We relate these results to current theories of conditionals.
Probability in reasoning: A developmental test on conditionals
Cognition, 2015
Probabilistic theories have been claimed to constitute a new paradigm for the psychology of reasoning. A key assumption of these theories is captured by what they call the Equation, the hypothesis that the meaning of the conditional is probabilistic in nature and that the probability of If p then q is the conditional probability, in such a way that P(if p then q)=P(q|p). Using the probabilistic truth-table task in which participants are required to evaluate the probability of If p then q sentences, the present study explored the pervasiveness of the Equation through ages (from early adolescence to adulthood), types of conditionals (basic, causal, and inducements) and contents. The results reveal that the Equation is a late developmental achievement only endorsed by a narrow majority of educated adults for certain types of conditionals depending on the content they involve. Age-related changes in evaluating the probability of all the conditionals studied closely mirror the developmen...
Children's conditional reasoning
Educational Studies in Mathematics, 1977
This study stemmed from a desire to redress the distorted view of mathematics in the elementary curriculum, created by the current imbalanced emphasis on computational rules and some applications, but very little logical analysis. The study is intended to show that fifth-grade students can significantly improve their use of logical analysis through a suitable instructional unit taught under ordinary classroom conditions. Concrete teaching materials were developed, through several trials and revisions, to familiarize students with the distinction between the valid inference patterns-Modus Ponendo Ponens and Modus Tollendo Tollens (AA, DC), and the fallacious ones-AffLrming the Consequent and Denying the Antecedent (AC, DA). No formal rules were taught. The experimental unit was implemented four to five times a week for 23-25 sessions, by 4 ffffth-grade teachers in their ordinary classes. The teachers participated in a twelvehour pretraining workshop. A pretest/posttest treatment/no-treatment design was applied to assess resulting improvement in students' conditional reasoning ability. The sample consisted of 210 fifth graders in a suburban area, 104 in 4 experimental classes and 106 in 4 control classes. A written group test was developed, through trials and revisions. Test items are formulated with a reasonable hypothetical content. Each item includes two premises: the first a conditional sentence, and the second either its antecedent, its consequent, or the negation of one of these, thus determining the logical form: AA, DC, AC, or DA. The question following the premises is stated positively. AA and DC are answered correctly by 'yes' or 'no': AC and DA by 'not enough clues' (NEC). The test contains 32 randomly-ordered three-choice items, eight in each logical form (two of the eight in each of the four possible modes in which negation may or may not occur in the antecedent or consequen0. No sentential connective other than negation and conditional appears in the premises. Test/retest reliability was 0.79.